In this paper, we partition the association rule set into disjoint equivalence rule classes. Each of them contains rules having the same confidence and then it is split into basic and consequence rule sets based on the order relation on it. Basic rule set, which includes minimal elements according to this relation, is directly found by our algorithm MG_BARS. In addition, by adding appropriate eliminable itemsets to both sides of basic rules in our algorithm MG_CARS, the consequence rules are completely and non-repeatedly generated and are confidence-preserved. Results of the experiments proved the efficiency of the above algorithms.